TS 967 
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Copy 1 



DEPARTMENT OF COMMERCE 



echnologic Papers 

OP THE 

Bureau of Standards 

5. W. STRATTON, Director 



No. 153 
AREA MEASUREMENT OF LEATHER 



FREDERICK J. SCHLINK, Associate Physicist 
Bureau of Standards 



ISSUED APRIL 24, 1920 




PRICE, 10 CENTS 

Sold only Or the Superintendent o( Documents, Government Printing" Office" 

Washington, D. C. 

WASHINGTON 

GOVERNMENT PRINTING OfFIQa 

1920 



•""ograph 



-',;•■*"*■* <-- '„, V-.! 3 ' 



DEPARTMENT OF COMMERCE 



Technologic Papers 

OP THE 

Bureau of Standards 

S. W. STRATTON, Director 



No. 153 
AREA MEASUREMENT OF LEATHER 



FREDERICK J. SCHLINK, Associate Physicist 

Bureau of Standards 



ISSUED APRIL 24, 1920 




PRICE, 10 CENTS 

Sold only by the Superintendent of Documents, Government Printing Offlce 

Washington, D. C. 

WASHINGTON 

GOVERNMENT PRINTING OFFICE 

1920 



Orkji v 






\o 



% 



x 



MAY 



8 1920 



AREA MEASUREMENT OF LEATHER 



By Frederick J. Schlink 



CONTENTS 

Page 

I . Introduction — Importance of the subject 3 

II. Types of area-measuring machines used in the leather trade 8 

1. The pin machine 9 

2. The wheel machine 13 

(a) Principles of operation 13 

(6) Typical designs 14 

( 1 ) Chain and lever totalizing gear 14 

(2) Differential gear totalizing system 17 

(c) Sources and determination of errors 19 

(1) Spacing of wheels 19 

(2) Width of rim 19 

(3) Overrun of wheelwork 22 

(4) Effect of thickness of material 28 

(5) Variance due to imperfections of the linkwork 30 

(6) Secular changes in hides and skins 35 

III. Methods of testing leather-measuring machines 35 

1. Form and material of the area standard 35 

2. Determination of machine performance 42 

3 . Acknowledgements 46 

IV. Summary 46 

I. INTRODUCTION— IMPORTANCE OF THE SUBJECT 

In January, 191 7, the Bureau of Standards, at the instance of 
the commissioner of weights and measures of the Commonwealth 
of Massachusetts, undertook the investigation of the methods and 
machines employed in the leather industry in the area measure- 
ment of hides and skins. Owing to the short time and limited 
staff available for the work, it was impossible to carry out the 
complete and exhaustive study of the field that its commercial 
importance would warrant. At the entrance of the United States 
into the war in April, 191 7, the whole of the staff and facilities of 
the Bureau were devoted to military work, which precluded all 
but the briefest and most cursory consideration of the problem from 
that time until the end of 191 8. Important and suggestive data 
were obtained, however, and some of these results are here pre- 
sented as of possible utility in relation to further studies which may 

3 



4 Technologic Papers of the Bureau of Standards 

be undertaken, and of service in guiding designers and users of 
leather-measuring machines in their choice of mechanisms and 
methods. As leather-measuring machines do not enter into direct 
relationship with the ultimate consumer, their operation has, in 
general, not been given the close supervision by weights and 
measures officials that is accorded the more common trade 
measuring instruments, such as weighing scales, capacity measures, 
and the like. On this account, up to the time of the investiga- 
tions reported in the present paper, no complete and suitable pro- 
cedure for conducting tests of leather-measuring machines had 
been developed; no tolerances were used, nor had any comparative 
study of types been made. 

The literature of this subject is very meager. The best mate- 
rial available up to the time of the investigation by the Bureau is 
to be found in "The Manufacture of Leather," by Davis. 1 The 
first edition of this book devotes a chapter of 1 2 pages to the subject 
of leather-measuring machines, including 13 figures and a list of 
United States patents issued in the interval 1790-1883, inclusive. 
The material of this chapter is almost entirely descriptive, cover- 
ing both obsolete and existing types of leather-measuring machines. 
No information is given as to the performance possibilities or 
comparative operating accuracies of the different types. 

In the 1897 edition of the above-named work the space devoted 
to leather-measuring machines is reduced to four and one-half 
pages by the elimination of a considerable amount of material 
descriptive of obsolete or undeveloped types of leather-measuring 
machines. In this edition, only two illustrations are given, one 
of a typical wheel machine and one of a pin machine. On account 
of the scarcity of satisfactory illustrations of leather-measuring 
machines, both of these are reproduced in the present 'paper. 
Tike the chapter in the earlier edition, the later treatment by 
Davis gives no information beyond descriptions of the machines 
and the manufacturers' claims for them. No adequate data of 
the sort required by the designer nor any indication of the sources 
and types of error to be expected are given. 

A pamphlet, "Suggestions to Sealers," issued by the depart- 
ment of weights and measures of the Commonwealth of Massa- 
chusetts, includes five pages regarding leather-measuring machines, 
comprising brief descriptions of the hand rack, the pin, wheel, and 
power machines, with suggestions regarding certain tests to be 
applied. 

1 Henry Carey Balrd & Co.. Philadelphia, 1885; 2d ed., 1897. 



Area Measurement of Leather 5 

The results of the Bureau's investigation, as comprised in the 
author's reports, were promptly and regularly forwarded to the 
Massachusetts commissioner of weights and measures, and by him 
transmitted to various representatives of the National Boot & 
Shoe Manufacturers' Association and the National Tanners' 
Association. The former association published in the report of 
the meeting of its executive committee of April 23, 191 7, an 
extended report made by the Bureau of Standards under date of 
March 30, 191 7, " On Certain Principles in the Design of Leather- 
Measuring Machines," which included a discussion of the prin- 
ciples of operation of the pin machine and the wheel machine, 
and an analysis of the sources of error of the latter, including the 
width of tires, spacirig of wheels, overrun of wheel work, effect 
of thickness of leather measured, and lost motion in the trans- 
ference chains. The same association also distributed leaflets 
comprising the report of February 5, "On the Form and Material 
of Standards of Area for Testing Purposes," and that of February 
12, which gives the results of an extended test upon which are 
based a great many of the conclusions regarding the serious 
inaccuracy of existing types of machines in service. The basis 
of this test was the measurement upon five different machines of 
five different calfskins ranging in area from 8.4 to 14.5 square 
feet. Readings were taken for each of these skins on each of the 
five machines, and the following tabular comparison was made 
with the actual areas of the five skins as determined by careful 
planimetric measurements conducted in the laboratories of the 
Bureau, careful correction being made for the shrinkage of the 
skins between the time of their measurement by the five meas- 
uring machines and their subsequent measurement by planimeter 
at the Bureau. This study also gave valuable data upon the effect 
of the overrun of wheelwork in occasioning serious errors of read- 
ing in excess. 

Some information as to the serious difficulties met with in connec- 
tion with these machines, as known to members of the leather 
trade, will be found in the January 18, 1917, and January 17, 1918, 
issues of the Shoe and Leather Reporter (Boston) . In the earlier 
article indication is given as to the amount of variation in meas- 
urement which is commonly found in the service operation of the 
usual measuring machines. The comparative measurements 
made upon the five different machines using five different skins, 
as referred to above, fully confirmed these opinions, and showed 
that, of the five machines investigated, the average errors ex- 



Technologic Papers of the Bureau of Standards 



tended over the wide range of 4.4 per cent in excess to 0.1 per 
cent in deficiency. 

TABLE 1. — Recapitulation of Comparative Results on Test of Five Leather- 
Measuring Machines, January, 1917 





Readings ol machine "A" 


Readings of machine "B" 


Serial number and 
actual area of skins 

(planimeter) 


First 
reading 


Second 
reading 


Average 
of first 

and 
second 

reading 


Reading 

at very 

low 

speed 


First 
reading 


Second 
reading 


Average 
of first 

and 
second 
reading 


Reading 

at very 

low 

speed 




12.87 
9.22 

14.87 
8.80 

13.35 


13.06 
9.20 

14.90 
8.65 

13.50 


12.96 
9.21 

14.88 
8.72 

13.42 


12.35 
8.80 

14.35 
8.22 

12.58 


12.45 
8.75 

14.40 
8.35 

12.90 


12.50 
8.80 

14.55 
8.35 

12.85 


12.48 
8.78 

14.48 
8.35 

12.88 




2: 8.88 


8.65 


4: 8.36 


8.37 












59.19 
+2.50 
+4.4 


56.30 
-.39 
-.7 






56.97 
+ .28 

+.5 











































Readings of machine "C" 


Readings of machine 
"D" 


Readings of machine 
"E" 


Serial number and 
actual area ol 
skins (planimeter) 


First 
reading 


Second 
reading 


Aver- 
age of 
first 
and 
second 
reading 


Read- 
ing at 

very 
low 
speed 


First 
reading 


Second 
reading 


Aver- 
age ol 

first 

and 
second 
reading 


First 
reading 


Second 
reading 


Aver- 
age of 

first 

and 
second 
reading 


1-1 12.40 

2: 8.88 

3: 14.46 

4:8.36 

5: 12.59 


12.45 
9.05 

14.60 
8.45 

12.75 


12.40 
8.95 

14.65 
8.40 

12.60 


12.42 
9.00 

14.62 
8.42 

12.67 


12.30 
8.80 

14.30 
8.20 

12.55 


12.70 
8.95 

14.63 
8.50 

12.80 


12.75 

8.80 
14.68 

8.50 
12.80 


12.72 
8.88 

14.66 
8.50 

12.80 


12.30 

8.90 
14.38 

8.50 
12.55 


12.45 
8.80 

14.48 
8.40 

12.55 


12.38 

8.85 
14.43 

8.45 
12.55 








57.13 

+.44 
+ .8 


56.15 

-.54 
-.9 






57.56 
+ .87 
+1.5 





















































The very great commercial importance of the problem can be 
indicated by the statement — for which the National Boot & Shoe 
Manufacturers' Association and the National Tanners' Associa- 
tion are the authorities — that the leather annually measured upon 
an area basis in this country amounts to 900 000 000 square feet, 
worth $450000000. All finished leather, including boot and 
shoe uppers, book, enameled, and upholstery leather, are sold 
upon an area basis, and such hides and skins all have their selling 
price determined by the use of leather-measuring machines. In 
fact, a single machine may determine the selling price of several 



Area Measurement of Leather 7 

million dollars' worth of hides per annum. One such machine, 
tested during this investigation and found to have a large error 
in excess, determined the sale of about $2 000 000 worth per an- 
num, and this large volume is believed to be no very unusual cir- 
cumstance, since in a large leather warehouse in another city a 
business of $8 000 000 per annum was being handled on two and 
occasionally three machines. Moreover, the unit value of the 
leather may be very high — $1.50 per square foot or even more. 
The Boot & Shoe Manufacturers' Association, in one of the reports 
referred to above, has stated that 3 per cent variations of meas- 
urement are common. This statement becomes the more signifi- 
cant when it is recalled that practically this means that 3 per cent 
errors are common, as the investigations have shown that the 
variations of leather-measuring machines are almost without ex- 
ception in the direction of excess measurement and the variations, 
therefore, distribute themselves all in the one direction from 
accurate measurement. 

At this writing, also, the question of leather measurement is 
becoming prominent in England, and it is reported 2 that the 
standardization of the superficial measurement of leather has been 
discussed with the Board of Trade by a deputation representing the 
Federation of Curriers and Light Leather Tanners, and the Federa- 
tion of Boot & Shoe Manufacturers, the former group representing 
the sellers and the latter the buyers. It appears that at the pres- 
ent time no law is in force in England by which dishonest meas- 
urement can be punished, and that little information is available 
regarding leather-measuring machines, while many users of such 
machines have no means of verifying their accuracy. The con- 
sumption of leather purchased by measurement in England is 
stated to be approximately 400 000 000 square feet per annum. 
Reference was made to the importance of protecting English buy- 
ers against inaccurately measured leather imported from abroad. 
Some discussion was given to the importance of the use of a tem- 
plate of the correct substance for carrying out tests and of adjust- 
ing the machine when changing the substance of the goods being 
measured. The speed of the machine was also mentioned as being 
important, and the statement made that the slow speed ' ' will tend 
to show greater surface than when the leather is rushed through," 
which is, of course, an error of statement so far as our knowledge 
of the conditions can determine, the effect of high-speed operation 

' Leather Trades' Review, Mar. 26, 1919; The Leather Manufacturer, May, 1919. 



8 Technologic Papers of the Bureau of Standards 

being just the reverse according to our own experiments. Atten- 
tion is called to the discrepancies due to shrinkage after glazing 
or laying in store. 

The writer has just had opportunity to read the brief discus- 
sion of the leather-measurement question which appears in the 
annual reports of the Director of the British National Physical 
Laboratory, 1913-1915, which, may be briefly abstracted as 
follows : 

Under the direction of Mr. Attwell and at the joint request of the Board of Trade 
and the Federation of Light Leather Trades, an investigation into the behavior and 
accuracy of power-driven area-measuring machines has been undertaken, and ma- 
chines in daily use tested at intervals. The secular variation in circular rubber tem- 
plates, used for testing the machines, has been investigated, and attempts have been 
made to age such templates artificially. 

The investigation begun in 1913 was referred to in the succeeding annual report as 
having been completed, and the conclusions briefly stated therein. The first was 
that "the machine should be controlled by means of reliable and suitable templates 
which should be of approximately the same area and thickness as the skins under 
measurement." It appears from theoretical considerations that errors from 0.16 to 
0.32 square foot must be tolerated with the different machines in use, although the 
errors found in practice exceeded the above figures, due largely to the fact that none of 
the machines was fully controlled by suitable templates. Reference is made to the 
necessity of providing in addition to the machine tolerance, an allowance to cover 
the shrinkage of the skins. It is stated that "it would appear to be impossible at pres- 
ent for a buyer to substantiate a claim against a seller in which the error on an in- 
dividual skin did not exceed one-half square foot, or in which the mean error on a 
consignment did not exceed one-fourth square foot per skin. These figures might 
be reduced to about one-half by the use of an improved type of machine. 

The shrinkage of area templates made of rubber fabrics is again discussed, and shown 
to amount to as much as 1 per cent in 15 months in laboratory storage, and in some 
cases templates which have been used in the field show shrinkage amounting to nearly 
2 per cent, most of which occurs in the early life of the template, suggesting artificial 
aging as a remedy. 

So far as the number of leather-measuring machines in use is 
concerned, practically no data are available. We are informed, 
however, that about 200 such machines of all types were in use 
in Massachusetts alone at the beginning of 191 7. 

II. TYPES OF AREA-MEASURING MACHINES USED IN THE 
LEATHER TRADE 

The types of leather-measuring machines known in the leather 
trade are four: 

1 . The hand frame — which is nothing but a screen divided into 
squares comprising one-fourth of square foot each, which is a super- 
posed upon the hide to be measured and by counting of the in- 
cluded squares — affords a means of estimating the area to some 
degree of acuracy, depending upon the skill of the user. This 



Area Measurement of Leather 9 

simple device is very little used at the present time because of its 
slowness and lack of precision, and the fact that it requires supe- 
rior skill on the part of the measurer. 

2. The pin machine, which provides for the weighing of a number 
of vertical rods or pins, the remaining pins in the group being 
relieved of communication with the weighing mechanism by the 
interposition of the hide being measured. 

3. The wheel machine, which is the power-driven type now in 
most common use, and which performs the function of measurement 
by the traversing of the hide under a bank of uniformly spaced 
narrow wheels whose several rotations due to the passage of the 
hide are then mechanically totalized. 

4. The planimeter, of which one or two special types of large 
capacity are available for the measurement of hides and skins. 
The planimeter, of course, gives a reading of area by manually 
tracing the outline or perimeter of the hide. 

The present use of the planimeter, it is believed, is limited to very 
few instances, and it practically does not enter into the commercial 
measurement of hides and skins, but only into the determination 
of unit costs as involved in the number of shoe elements which 
can be cut from a known area. The planimeter will also be use- 
ful in standardization work, as in checking area standards used 
in the testing of ordinary leather-measuring, machines and, pos- 
sibly, for the routine measurement of high-priced leather; its 
utility for the latter purpose depends upon a study of the eco- 
nomics of the operation, the cost of measurement being offset 
against the cost of the errors which may characterize competing 
instruments for the same purpose. 

1. THE PIN MACHINE 

The pin machine, which is no longer manufactured but of which 
a few examples built 25 years ago or more are still in operation, is 
illustrated in Figs. 1 and 2, and its construction and operation are 
as follows: A frame is supported pivotally by a knife-edge at 
the rear, and is so counterbalanced as to be lifted easily into and 
out of parallelism with the table upon which, in the first illus- 
tration, it is seen to rest. A part of the frame is connected by a 
cord to the load-supporting system of a suspended spring balance 
suitably hung in position above the table and the inclinable frame. 
The frame is made up of light wooden strips perforated at uniform 
intervals, and arranged in lines parallel to the plane of the spring 
balance seen in the illustration. Through each of the perforations 
150918°— 20 2 



io Technologic Papers of the Bureau of Standards 

a metal pin passes, loosely projecting some distance beyond the 
lower surface of the frame, and prevented from dropping through by 
an eye or head at its upper end. The table over which the frame 
is supported is made up as a grid of wooden strips perpendicular to 
the plane of the spring scale. The spacing of the bars in the grid 
is such that the pins coming through the frame above pass into 
the interstices and do not touch the grid itself. The lower ends 
of all the pins thus pass into the slots formed in the table, and all 
stand at the same level. 

Thus, when all the pins are hanging through the slots in the table 
as described, their weight is carried by the suspended frame, sup- 
ported in part by the pivot on which that frame turns and in part 
by the spring balance to which its front bar is connected. The 
spring balance, therefore, is in equilibrium under the load, and 
in this position may be said to register zero area. If, now, the 
frame is raised, a sheet of leather placed upon the table or grid, 
and the frame again lowered, so that it is parallel and close to the 
table though not in contact with it, those pins below which a por- 
tion of the leather is lying will be raised by it and will slide up- 
wardly through the holes in the inclinable frame in such manner 
that their weight is no longer carried by it, as their weight is now 
received and supported by the leather rather than by the ring or 
head from which they are normally hung. There are thus some 
pins which are supported by the inclinable frame from the shoul- 
dered portion at their upper ends (the ring or head mentioned 
above), and some are supported by the leather, which lifts the 
shouldered portion out of contact with the inclinable frame by 
contact with their lower ends. The frame being thus relieved of 
the weight of the latter group of pins, the spring balance will change 
its reading in direct proportion to the number of pins which no 
longer pass into the slots of the grid but are supported by the 
leather, the pins being so proportioned that their weight varies 
inversely as their distance from the pivot about which the frame 
turns, so that each pin exercises the same turning effort about that 
fulcrum. This adjustment is accomplished by making the pins of 
the various rows of decreasing length and diameter, as may be con- 
venient to gain the desired weight gradation. The spring balance, 
being graduated in units of area in a reverse direction from the 
ordinary weight graduation, gives increasing readings of area for 
what corresponds to decreasing values of weight of the pins sup- 
ported by the frame. Simple means for changing the weight or 
turning moment of the inclinable frame are provided so that the 



3ureau of Standards Technologic Paper Mo. 153 




Fig. i 




Area Measurement of Leather 1 1 

scale may be made to indicate a zero reading when the pins all 
hang through the slots in the grid below — that is, when no leather 
is in place for measurement. 

Obviously, if the number of pins could be indefinitely large (or, 
conversely, their spacing indefinitely close) an exact determination 
of the area to be measured would be obtainable in this way, were 
it not for the friction which would be introduced at the points 
where the pin slides against the guiding holes in the supporting 
frame. The degree of approximation thus increases with the 
closeness of the spacing of the pins in the frame. On machines 
of this type which were examined during the investigation, the 
spacing of the pins was for some unknown reason different in the 
two perpendicular directions, being 2 inches in a direction parallel 
to the plane of the spring balance shown and 1 } A inches in the direc- 
tion perpendicular to this plane. In practice, the friction of the 
pins passing through the frame, though they were very numerous, 
appeared to be so small as to be negligible, and no difficulty was 
had in obtaining readings which appeared to be quite free from 
errors due to this cause, as the spring balance would oscillate quite 
freely and for a considerable time after the frame was lowered to 
the table. 

It would seem that if a well-constructed weighing scale is used, 
this type of machine should offer the possibility of very satisfac- 
tory accuracy when the pins are closely spaced. The use of a 
spring balance is no way essential, as almost any desired type of 
weighing scale can be employed for indicating the change in the 
weight carried by the frame. 

In the book by Davis, above referred to, a machine having a 
similar essential principle of operation is described, but it is not 
known to what extent this type of machine came into use. It is 
the invention of Williams, Moore, and Hulburt, in 1879, and the 
weighing of the pins is carried out by the reception of their lower 
ends upon a weighing scale platform mounted below what corre- 
sponds to the grid or table described above. Under this system 
the pins which pass through and are not supported by the leather 
are allowed to exercise their effect upon the weighing scale, and 
the result is read upon a dial as in the device described in greater 
detail above. In this case, as before, the weight indicated corre- 
sponds directly to the area which is not covered by the leather, the 
reduction to area of leather being carried out by a reverse scale of 
graduations, as has been indicated. This machine is equipped 
with a sort of brake designed to check the oscillations of the weigh- 



1 2 Technologic Papers of the Bureau of Standards 

ing system before the reading is taken. It should be noted that 
in this type of construction, the pins do not touch the holes through 
which they pass, at the moment when the weighing operation is 
being performed, as in this position the pins are left resting free of 
their guiding holes, supported upright by flat end surfaces, either 
on the surface of the leather or on the surface of the weighing 
table below it; moreover, in this machine the pins are not required 
to vary in weight but are all uniform, as the system on which they 
are weighed is a true weighing scale having a platform moving 
parallel to its initial position instead of rotating about a fixed point. 
The indications are therefore independent of the position of the 
, applied load. 

The author has often heard the statement that the pin 
machine is inaccurate for the reason that it is subject to varia- 
tions due to changes in the atmospheric humidity, temperature, 
etc., as affecting the dimensions of the wooden frame. As a 
matter of fact, this defect, the importance of which has doubtless 
been overestimated, is not peculiar to this type of machine, but 
to the materials of its construction, and can be made quite negli- 
gible by the use of other material for the framework. In fact, it 
would be quite possible to use a metal framework having a small 
or negligible coefficient of expansion, so that the apparatus would 
be even less affected by temperature changes than are the existing 
types of wheel machines. 

The advantages of the pin machine are obvious. It is simple 
in construction, cheap to manufacture (its cost should not exceed 
one-third to one-half of that of the wheel machines), it affords 
possibilities of very satisfactory accuracy when a sufficiently large 
number of pin elements are used, and it eliminates, moreover, 
many of the sources of error common to the wheel machines as, 
for example, that due to overrun of wheelwork, that due to the 
width of tires (the analogous error is of no moment in the pin 
machine, since the area of the ends of the pins can be very small) , 
and that due to the thickness of the leather. The disadvantages 
principally raised in objection to this type of machine are, first, 
that it is slow in operation; and, second, that it does not take 
account of the area involved in the concavity or bellying of the 
hide. 

So far as the first objection goes, it is believed to be overdrawn. 
The author, in a few observations made without special prepara- 
tion, upon the use of the pin machine in comparison with the 
wheel machine, • each in the hands of an experienced operator, 



Area Measurement of Leather 



13 



found that the former required not more than 30 per cent more 
time per skin than the latter (pin machine, 12 seconds per skin; 
wheel machine, 9 seconds per skin) ; this despite the fact that the 
wheel machine was clearly overspeeded, as were most of the wheel 
machines observed. (See under Overrun of Wheelwork, below. As 
explained more fully in that section, any rational comparison of 
the speed of operation of the two types will require that the wheel 
machine be operated at a speed known to be low enough that the 
overrun error does not exceed a suitable small tolerance.) An 
item in a Peabody, Mass., newspaper refers to a competitive trial 
between the pin machine and the wheel machine, and actually 
credits a higher speed of operation to the former. 

2. THE WHEEL MACHINE 

(a) Principles of Operation. — The wheel machines operate 
upon a different principle, which may be briefly described by 
reference to the appended sketch (Fig. 3) representing any desired 




Fig. 3 

irregular area. Imagine that parallel lines be drawn upon such 
an area dividing it into strips of uniform width. The area of 
each strip will then be given by the product of its width into its 
average length and the area of the whole figure by the common 
width of the strips multiplied by the sum of the lengths of all the 



14 Technologic Papers of the Bureau of Standards 

strips. Now, if the irregularities of the outline to be measured 
are not marked by sharp discontinuities, the average length of 
each strip is determined approximately by the length of its 
middle line or median, and it is upon this assumption that the 
operation of the wheel-type machine is based. The measurement 
is carried out mechanically somewhat upon the following principle : 
The irregular area to be measured is drawn through the machine 
by a feed-roll, the construction being such that the leather in its 
passage produces rotation of the members of a series of parallel, 
uniformly spaced wheels when, and only when, leather is in 
contact with and passing under such wheels. Bach wheel, 
therefore, rotates through an angle which is proportional to the 
length of the middle line of the strip which extends on each side 
of that wheel a distance equal to half the space between the 
wheels. If now, the rotations of the several wheels are totalized 
and that sum is multiplied by a constant, the result will be in 
units of area, and will represent an approximate integration of the 
irregular figure measured. 

(b) Typical Designs. — (z) Chain and Lever Totalizing Gear. — In 
the actual construction of the wheel machine, an old model of 
which is shown in front elevation in Fig. 4 and in transverse sec- 
tion in Fig. 5, the roller B, which extends the full working length 
of the machine, rotates continuously clockwise. The wheels, A, 
which are the uniformly spaced, parallel wheels referred to above, 
rotate by frictional engagement with B, a small clearance being 
allowed between the pinion affixed to the axis of A and the seg- 
mental gear, C. If, now, a hide be inserted between B and A, 
wheel A is slightly lifted, the axis of B being fixed, and the pinion 
affixed to A at once engages the segment C, causing C to rotate 
clockwise until the extremity of the strip over which A is passing 
has passed out from between A and B. At this instant A drops 
back into contact with B and the pinion on A is thereby disen- 
gaged from C, whereupon the pawl seen in the figure prevents 
retrograde rotation of C. Segment C, then, in each case describes 
an arc proportional to the length of the median of the correspond- 
ing strip of the hide. 

The travel of the several segments C (or in some cases complete 
gears, performing an identical function) is totalized by a system of 
chains passing over pulleys mounted on levers, the lever system 
being so arranged that the contribution of motion due to the wind- 
ing up of individual chains on the drums affixed to the center of the 



Bureau of Standards Technologic Paper No. 153 




Fig. 4 




Fig. 7 



Area Measurement of Leather 



15 



segments C, is transmitted in reduced amount, but in equal reduc- 
tion for every chain, to a single rack or segmental gear / ' driving 




Fig. s 



A, traversing wheel carrying at its center the traversing wheel pinion; B, feed roll; C, accumulating seg- 
ment (or gear); M, pawl restraining retrograde movement of C until machine is zeroized by lifting all 
pawls; and N, transference chain. 

the pinion of the indicator at which the reading is obtained. In 
brief, then, the lengths of the several parallel medians of the irregu- 



i6 



Technologic Papers of the Bureau of Standards 



lar area are measured individually by the rotation of uniformly 
spaced wheels, and the amount of motion of these several wheels is 
totalized by a suitable lever system and, finally, through a suitable 
rack and pinion movement, registered upon a dial. 

The next figure shows a typical lever system by which the uni- 
form reduction of displacements is carried out. It will be observed 





«rf"| 










W* 






^"0 




<^, fl" 










a? |WV' 




j2Z-l 










Altar 


3C^C ^ 2 ' 


-&=£[=^ 


&*js* 




yys- 


w" 




) f t — (£)»vv 




-yyy. f 






3*i.\VJ /IK vv 1 


(oj (* 















w% 




that this leverage is so arranged as to produce the same reduction 
of movement of any chain when measured- at the point d 12 . Detail 
dimensions of the lever system by which this end is obtained need 
not be cited, as a suitable arrangement can always be designed 
upon the well-known principles of the simple lever. 

When it is desired to reset the pointer to zero to permit the 
measurement of another skin, a bar engaging all of the pawls above 
mentioned is operated, disengaging the pawls from contact with 
the segments and permitting the segments to return to their lower- 
most position, propelled by their own unbalanced weight. Leather 
bumpers are usually included to assure uniform and shockless stop- 
page of the segments, as they return to their zero position. Machines 
of this type are usually graduated to 30 square feet by increments, 
of one-eighth or one-fourth of a square foot. A few machines have 
a capacity of 60 square feet by one-fourth of a square foot. 



Bureau of Standards Technologic Paper No. 153 





Fig. 9. — Typical wheel type leather -tneasttrinq machines 



Area Measurement of Leather 17 

In another design, operating upon this same general principle, 
the segments, C, are extended to full circles with teeth over the 
whole circumference. Instead of permitting these wheels to revert 
to the initial position, the machine is zeroized by unclutching the 
winding drums at the centers of these gears and restoring the drum 
itself to its initial position. This method is designed to eliminate 
the wear of the segmental gears used in the other type, which is, 
of course, greatest at the portions of the circumference near the 
initial position of engagement. The use of continuous forward 
rotation of the accumulating gears is, however, associated with a 
disadvantage, in that the use of a balanced gear definitely aggra- 
vates the error due to overrun of wheelwork, as will appear in the 
later discussion. 

(2) Differential Gear Totalizing System. — Another type of totaliz- 
ing train only recently developed and not yet ready for the market 
is based upon the principle of differential gearing. The appended 
Fig. 10 illustrates the arrangement used in an early model of this 
machine. Eack measuring wheel is pivoted between a pair of 
narrow-tired disks which are rotated by the feed roller, and serve 
to smooth and direct the skin as it passes through. As in the 
machines using the chain-and-lever totalizing gear, the measuring 
wheels rise at the entrance of the skin, due to its thickness, and 
thereby effect engagement with accumulating gears. These gears, 
however, are not associated with a winding drum but engage in 
pairs with a differential gearing homologous to that used in the 
rear-axle assembly of an automobile, except that its function is 
fulfilled by the use of a compact arrangement of spur gears only, 
obviating the use of bevel gears. 

To understand the manner in which this gearing is used to effect 
the totalization, consider an ordinary automobile of which the 
speed-change gears are in neutral or the clutch disengaged, the 
rear wheels being jacked up. If now the right-hand rear wheel ih 
held stationary and the left wheel turned m revolutions, the clutcs 
shaft or "propeller " shaft will rotate through some other number, 
say n, of revolutions, depending upon the gear ratio of the car. 
Similarly, if the left-hand wheel is held stationary, and the right- 
hand wheel rotated m revolutions, the clutch shaft will rotate 
through the same number n revolutions. If, however, both rear 
wheels are rotated in the same direction the same number of revo- 
lutions m, the propeller shaft will be found to rotate through twice 
as many revolutions as before, namely 2-n, and this will be the case 
150918°— 20 3 



1 8 Technologic Papers of the Bureau of Standards 

whether the m revolutions described by each of the two rear 
wheels takes place simultaneously, or successively, or at the same 
or different rotational speeds. If the right-hand wheel rotates 
through a different number of revolutions than the left-hand 
wheel, the number of revolutions of the propeller shaft will be pro- 
portional to the sum of the rotations of the two wheels, also with- 
out regard to whether or not the rotations were carried out at the 
same time and at the same speed. 

An exactly similar sort of summation takes place in the type 
of leather-measuring machine now under discussion. If one trav- 
ersing wheel is rotated, and the other of that pair remains station- 
ary, no leather passing under it, the intermediate totalizing shaft 
A rotates only half as far as it would were both members of the 
pair rotated by the same amount; and when the rotations are 
unequal in amount, the intermediate shaft A rotates by an amount 
which is proportional to the sum or the average of the rotations 
of the two members of the measuring pair. 

The measuring wheels are thus grouped in pairs throughout 
the machine, and the intermediate totalizing shafts similarly 
"feed" their several rotations by pairs into superior intermediate 
totalizing systems, until finally after several collections and aver- 
agings, the rotation is transmitted to the dial mechanism, which 
receives a movement proportional to the average and hence to the 
summated movement of all the measuring wheels. 

As in other wheel machines, a ratchet and pawl are provided to 
prevent retrograde rotation, which in this case would be induced 
by the reaction effect of adjacent gear trains. In addition to 
the usual dial for registering the area of the individual skins, 
this machine provides a counter to record the number of skins 
measured, this being operated by the action of resetting; and an 
integrating dial, to show the total area of all skins measured. 
In the machine shown, the measuring wheels are spaced only half 
as far apart as in the types already described. Other things 
being equal, this affords, as will appear later, a considerable im- 
provement in the accuracy of approximation to be attained in 
the measurement. 

Some reference has been made in conversations with the author, 
to a type of wheel machine in which radial pins carried in the 
several traversing wheels are depressed by the contact of the 
hide and by that depression engage a suitable accumulating 
mechanism. So far as is known, only one such machine has been 
brought into this country, and information about its operating 



Area Measurement of Leather 19 

principles and performance is very meager. It has been said 
however, that the particular machine imported was not success- 
ful, owing to extreme delicacy of mechanism, necessitating 
frequent adjustment or repair. 

(c) Sources and Determination of Errors. — (/) Spacing of 
Wheels. — As can be easily understood without special explana- 
tion, the accuracy of approximation in the integration of an irreg- 
ular area by the principles exemplified in the wheel machine is 
increased as the distance between the parallel measuring wheels 
is decreased. The practical considerations involved in the me- 
chanical construction, such as the necessary clearance between 
neighboring parts and the cost of manufacture, will set a limit 
upon the closeness of spacing possible. The distance between 
centers of the rims of measuring wheels in the types of machines 
now commonly used, is \% inches. 

One point of importance to be noted in connection with the 
errors due to insufficiently close wheel spacing is that when a 
tolerance of error is established upon the area measurement 
carried out upon the machines and a certain fraction of this error 
is allotted, as is requisite, to that due to the spacing of the wheels — 
the maximum wheel spacing permissible, to insure accuracy 
within this limit, can be closely calculated when a suitable outline 
or type of the area to be measured is determined upon and estab- 
lished as a standard for the purpose. H. M. Roeser, of the Bureau 
of Standards' staff, has given careful study to the relation of the 
closeness of spacing of the measuring units to the accuracy of 
, area approximation, and is in a position to advise in detail as to 
the methods to be followed by the designer of a leather-measuring 
machine with respect to this phase of the problem. Obviously 
the magnitude of the error due to interval between wheels is a 
function of the irregularity of the outline of the hide. The more 
smoothly outlined the figure, the greater can be the interval be- 
tween measuring wheels, for a given allowance of error, while an 
extremely jagged perimeter might require three or four times as 
many wheels per unit of machine length to permit of attaining the 
same degree of accuracy. Therefore, we find in this consideration, 
as in others to follow, a compelling reason for the adoption of a 
standard form of test area, a matter which fortunately raises no 
important practical difficulties. 

(2) Width of Rim. — The next source of error is also dependent 
upon the shape or figure of the area measured. It will be recalled 
from the general discussion of this type of machine that it is the f unc- 



20 Technologic Papers of the Bureau of Standards 

tion of the measuring wheels to measure the middle ordinate of the 
strip which each wheel traverses. This could be done with perfect 
accuracy only by a wheel with an infinitely narrow contact surface 
or rim, and any approximation to this requirement is, of course, 
impracticable with present designs, because of the necessity of 
getting sufficient traction to drive the relatively heavy and 
resistant mechanism by tractive contact between the periphery of 
the wheel and the surface of the hide to be measured. 




Fig. ii 

Fig. 1 1 shows how a finite width of rim of the measuring wheel 
results in an exaggeration of the movement of the traversing 
wheels. If AB is the middle line of the strip which wheel DC is to 
measure, its length can be correctly measured only by a wheel 
which travels along the line AB and touches that line only. If 
the wheel has width, it touches a zone of which AB is the median, 
and continues to turn until every part of its tire has left contact 
with the hide, or in the sketch, ADFCE being the plan view of an 
exaggeratedly wide-rimmed wheel, until the point C of the wheel 
and C of the hide leave contact (the thickness of the hide being 
neglected for the moment, this being a cause of additional delay 
in the completion of the traverse) . Thus the ordinate of the hide 
is overmeasured by the amount EC which represents the excess 



Area Measurement of Leather 21 

of rotation of the wheel consequent upon the existence of driving 
contact outside the median line of the strip. 

It will be noted that this effect, which is an important one, 
invariably tends toward overmeasurement, and that like the pre- 
ceding type of error it is the more in evidence on irregularly or 
jaggedly outlined hides, since on such hides the difference between 
the middle ordinate of any strip and the longest ordinate within 
the purview of the measuring wheel is enhanced. The magnitude 
of this error for any given width of tire, as with the wheel spacing 
in the preceding section, is easily calculated, and when a limit is 
set upon its contribution to the total error of the machine the 
maximum allowable width of the wheel rim is readily established, 
a standard form of area again being postulated for the purposes 
of the investigation. 

As has been suggested, this type of error indicates a very 
definite and desirable trend in the design of leather-measuring 
machines, namely, that the frictional and other resistances shall 
be reduced to the lowest possible value, to the end that a mini- 
mum of traction shall be required to drive the measuring disks. 
Reduction of the driving traction will proportionately reduce the 
width of wheel rim required, with a consequent improvement in 
the performance of the machine. There is no reason whatever 
to suppose that the modification here suggested will offer any 
serious technical difficulties, although, to be sure, it does involve 
to some extent the simplification of mechanical detail, as it is 
eminently desirable that the number of moving parts- be reduced 
in order to make available the most potent means of obtaining 
the desired reduction in the driving force required. The use of high 
normal unit pressure between the wheels and the leather to obtain 
the necessary traction is, of course, out of the question, as that 
method would involve serious danger of marking and disfiguring 
the finished surface of the skin. 

With regard to the matter of excessive width of traversing 
wheel rim, it may be noted that the author had opportunity to 
examine one model of a leather-measuring machine in which the 
traversing wheels or what corresponded to them, were constructed 
as a bank of rolls, filling in all the space available, so that the 
exaggeration of rim width had been carried to its highest possible 
limit, the width of each rim thus being equal to the center to center 
distance between traversing wheels. This is indicative of a num- 
ber of features which would permit the user of a leather-measuring 
machine to obtain increased reading on hides and skins, while the 



22 Technologic Papers of the Bureau of Standards 

machine would still pass the usual accuracy tests applied. It will, 
of course, be understood that such a wide-rim machine as has 
been described would give accurate results on a rectangular test 
pattern, if this pattern were passed through normally, without 
being inclined to the common axis of the traversing wheels, 
though when passed through slantwise the excess of reading 
should be very apparent. 

(j) Overrun of Wheelwork. — In all wheel machines, there will be 
some error due to the delay of the accumulating gear in picking 
up the velocity corresponding to the movement of the hide passing 
under it, since the wheel must be accelerated from rest by the 
pinion of the traversing wheel at the moment the latter has made 
contact with the hide. After the hide has passed out from con- 
tact, the accumulating wheel will tend to continue its rotation 
and will so rotate until its kinetic energy is absorbed by the 
frictional resistances of the mechanism and by such restoring or 
counterforces as are present, such as counterbalance weights, or 
unbalanced wheels or segments. 

This error is quite large in some of the existing wheel machines, 
and it should be especially noted that it can not be considered as 
of small importance on the supposed ground that it will produce 
an error of constant amount in excess, and will, therefore, be 
cared for in the calibration of the machine. Even if the error 
were constant, either absolutely or relatively, at any speed, 
proper control of the machines would then require that a sensitive 
and reliable speed indicator or tachometer be part of the equip- 
ment. The only possible means for correction of this error, if it 
could be rectified rigorously, would be the setting of the pointer 
so that it would start back of the zero point, the retrograde shift 
of the zero being made equal in amount to the determined value 
of the overrun error. This is manifestly impracticable even 
under the best conditions, even if it were not for the fact that the 
error is not constant but a function of the outline or figure of the 
hide as well as of the number of wheels operative in a given 
measurement. The reason for this is clear; every time the 
traversing wheel pinion is lowered out of engagement with the 
accumulating gear, the latter spins forward a certain more or 
less definite amount, depending upon its previous rotational 
velocity, its moment of inertia, and the resistances of friction and 
gravity and other forces which oppose its movement. Now if 
the outline of the hide is such that a given accumulating gear is 
engaged and disengaged a second time in the traverse of the hide, 



Area Measurement of Leather 23 

the error is doubled, approximately, due to the second oppor- 
tunity of the wheel to spin ahead of its proper final position of 
rotation. 

Experiment has shown, as will be seen on page 24, that every 
increase of speed of rotation will produce an increase in the 
readings of area obtained, and when once the contribution to 
the total error or variance of the machine that is deemed per- 
missible as resulting from this cause alone, is decided upon, the 
correct limiting speed of operation can readily be determined by 
experiment. To do this, the machine will be operated with the 
same standard of area or with the same series of standards, 
beginning with a very slow speed of operation, so low that the 
overrun error is quite negligible, and increasing by steps to some 
higher speed. A curve will then be plotted with the actual speed 
of rotation as abscissas, and the increase of reading over the 
reading corresponding to the initial very slow speed as ordinates. 
The value of the speed of rotation corresponding to the point where 
this curve crosses the horizontal line defining the permissible 
limit of error due to overrun effect alone will be the maximum 
allowable rotational speed. Its determination in the manner 
described will present no difficulty. If there should be any 
doubt as to the observance by the user of this proper maximum 
speed, it would be quite possible to apply a speed-limiting governor 
so arranged as to make the machine inoperable above the prede- 
termined speed for which it has been adjusted. 

There appear to be very considerable differences between the 
amounts of the overrun error of the several existing types of 
machines, and this can be accounted for in part by the fact that 
in one type the accumulating gears are in balance, and their rota- 
tion is, therefore, opposed only by frictional resistances and by 
the counterbalance weight provided at the dial end of the mech- 
anism to take up backlash. On the other hand, the accumulating 
gears of another make are not in balance but are formed as seg- 
ments, so affording a considerable restoring moment to oppose 
the continuance of the forward rotation. In a later modification 
of the latter machine, the accumulating gears, while not seg- 
mental, are nevertheless designed to be somewhat out of balance, 
and this has a similar though perhaps an insufficient effect. This 
unbalance is sufficient to, and is used to return the parts of the 
machine to their zero position after the completion of a measure- 
ment, which it does by causing backward rotation of the accumu- 
lating gears under the action of gravity, upon the release of the 
system of pawls which engage these gears. 



2 4 



Technologic Papers of the Bureau of Standards 



It is the opinion of the author that the overrun error is decidedly 
excessive on all types of existing wheel machines, even when these 
machines are run at the lowest speeds now in commercial use, 
and there is little doubt that, in some instances, wheel machines 
have been deliberately overspeeded to produce overmeasurement. 
At least one instance has been reported of a wheel machine being 
regularly run at ioo per cent above its rated operating speed, a 
procedure which must unavoidably produce enormous errors due 
to overrun. 

Definite numerical results on the overrun error are given in 
the table below, the first three machines being wheel machines — 
two of one make and one of another — and the last two machines 
being pin machines. The second column under A is significant 
in that it clearly bears out the statements made above in the 
present section, that the overrun errors are increased by a manner 
of use of the' machine which permits the accumulating gears to be 
engaged and disengaged more than once in the traverse of a single 
skin. It will be seen that the values in column 2 for machine A 
are very definitely higher than those in column 1. It will be 
understood that in passing the skin through the machine with its 
long axis perpendicular to the axis of the feed roll, the wheels at 
the limits of the area to be measured will naturally be lifted and 
lowered a number of times on account of the serrated nature of 
these two corresponding portions of the hide perimeter. 

TABLE 2.— Readings on Skin No. 6 
[Test No. 20725. All readings of area in square feet] 





Actual 

of skin 
No. 6 

(planim- 
eter) 


Readings on machines designated as — 




A ■ 


B 


C 


D 


E 




Condi- 
tion li 
Speed 
normal 


Condi- 
tion ;:'■ 
Speed 
normal 


Condi- 
tion la 
Speed 

12 
r. p. m. 


Speed 
64 


Speed 
30-60 


Speed 
18 


Speed 
normal 


















8.74 


8.70 


9.00 


8.65 


8.80 


8.62 


8.50 


8.75 


9.00 


8.70 






8.85 


8.90 


8.65 


8.75 


8.62 


8.50 


8.62 


8.95 


8.80 






8.80 


8.88 


8.62 


8.75 


8.75 


8.62 


8.65 


9.00 


8.70 






8.88 


9.00 


8.62 


8.63 


8.75 


8.50 


8.75 


8.90 


8.90 






8.95 


8.85 




8.82 


8.75 


8.52 




8.90 


8.75 












8.75 


8.50 


8.64 


















8.75 


8.60 


8.62 
















8.75 


8.58 


8.60 












9.03 




8.75 


8.62 


8.50 












8.90 


8.90 




8.75 


8.55 


8.60 
















Average 


8.74 


8.85 


8.93 


8.64 


8.75 


8.63 


8.56 


8.69 


8.95 


8.77 






+ -11 

+ 1.3 


+ .18 
+2.2 


- .10 
-1.1 


+ .01 

+ .1 


- .11 
-1.3 


- .18 
-2.1 


-.05 
-.6 


+ .21 
+2.4 


+ .03 






+ .3 









Area Measurement of Leather 25 

It was noted that the error due to overrun tends to be greater 
(absolutely, if not relatively) the larger the skin measured. In 
the case of one series of measurements made with a large skin on 
machine A , the following results were obtained : 

Reading of area at 14 r. p. m square feet. . 22. 33 

Reading of area at 59 r. p. m do. . . . 23. 21 

Difference do +.88 

Difference in per cent +3. 9 

Readings were also taken with the same machine using a rectan- 
gular sheet of leather, the area of which was determined by meas- 
urement and calculation to be 9.S6 square feet. The mean of 20 
readings on this machine was 10.08 square feet, the error thus being 
2.2 per cent in excess at normal running speed, even for a rectangu- 
lar outline, which, as has been shown, rather favors a low value of 
this particular error. 

Additional data on this question are available in Table 1, in 
which it will be seen that each of the power-driven machines shows 
a decided change in reading when its speed is reduced from that at 
which it has been regularly run to a very low speed ; this, of course, 
being proof direct that the wheel machines considered have all been 
run at a speed higher than is proper. The following brief analysis 
will show the amount of this difference : 





Errors and differences in per cent of true area 


Machine 


At normal speed 
of operation. 
Average error 


At slow speed 
of operation. 
Average error 


Difference 


A 

B 

C 


+4.4 
+ .5 
+ .8 


-0.7 

- .2 

- .9 


S.1 
.7 

1.7 



It is well to emphasize the fact that this fault can not, as has 
been assumed by manufacturers, be corrected in any given ma- 
chine by running it at that speed which would result in a zero error 
in a particular skin (or test sheet) , since the effect is, as has been 
shown, dependent upon the outline or figure of the skin, and the 
apparent zero error so obtained could not possibly be reproduced 
in succeeding measurements on other skins. As has been stated, 
the only remedy is to determine for each type of machine that 
speed at which the error due to overrun becomes equal to the par- 
tial or constituent tolerance allowable for that error. 



26 Technologic Papers of the Bureau of Standards 

In the absence of more exact information regarding the moments 
of inertia and opposing resistances of the accumulating gears of the 
wheel machines, the speed rating of such machines should be based 
not upon the number of revolutions per minute of the feed roll, as 
has been common, but upon the circumferential speed of that roll, 
thus affording a comparison of the rates of translation or traverse 
of the hide or skin to be measured, which is, of course, the funda- 
mental and useful basis for comparison of operating speeds. 

The author can not but believe that the emphasis placed upon 
speed of operation of these instruments is decidedly a fallacious 
one. It is his opinion that the cost of measurement, in so far as it 
appears in the cost of labor of the measuring machine tender, per 
square foot of area measured, is a factor of much less importance 
than the cost of inaccurate and variable measurements, or differ- 
ently expressed, the cost to a tanner or shoe manufacturer of 
seriously deficient or excessive measurement, such as there is 
every reason to believe existing machines will customarily and 
regularly give, may be so great that the speed of performing the 
measurement practically drops out of consideration. It might 
even be economical, in the case of valuable leather, to carry out 
the measurements by the use of a planimeter, when it is considered 
that the difference between successive readings on the same 
machine may amount to more than 4 per cent (see Table 4) , which 
in the case of a single skin of 15 square feet area, might amount 
to a money loss oi nearly a dollar. When it is considered that this 
measurement is performed in a few seconds, it appears absurd to 
emphasize labor cost and to ignore the cost of machine error. 
Even at the present high prices for labor, a great many skins can 
be measured for $1, even b} r the most slow, painstaking, and 
accurate method available. The writer, whose viewpoint, to be 
sure, is that of one outside the leather industry, and who may, 
therefore, be inadvertently ignoring some essential facts or diffi- 
culties inherent in the situation, is convinced that the emphasis 
which has been placed upon the speed of measurement (at the 
cost of accuracy) is essentially a false one, and that steps should 
be taken to study the economics of this situation from an engi- 
neering point of view, in order to determine with assurance, to 
what extent slowing up of the process, if it result in enhanced 
accuracy of measurement, will be economical. This problem is a 
perfectly definite and determinate one and the studies which it 
will require can be conducted at very small expenditure of time 
and effort. It will then be possible to give proper weight to the 



Area Measurement of Leather 27 

opposing factors of speed and accuracy, which now seem to be 
antagonistic. 

One expedient, which may already have been proposed, by 
which the overrun errors can be very largely eliminated, would be 
the use of a brake or dog so arranged as to come into operation the 
instant the traversing wheel has dropped back into contact with 
the feed roll. Within certain limits, of course, a brake of constant 
application, having for its purpose simply to increase the torque 
required to rotate the accumulating gears, would be of service. 
It would be necessary that it should not increase the energy 
required to operate the machine sufficiently so as to make slipping 
between the traversing wheels and the skin imminent or, collater- 
ally, to require a widening of the rims or increase of the contact 
pressure of the traversing wheels. There is some doubt whether 
practically the application of the braking arrangement would 
pay, since unless constantly in operation it would unavoidably 
add complication to the mechanism, a result which might be 
sufficiently detrimental to offset the relatively small advantage to 
be gained. All consideration of this question by the author has 
seemed inescapably to lead to the one conclusion, namely, that the 
only effectual expedient, if wheel machines are used, is to lower 
the speed of traverse to the required value, however low an oper- 
ating speed that may involve. Thus, if the manufacturer is 
required to specify the speed of operation of his machine in feet 
per minute of passage of leather, that speed being sufficiently low 
that the partial tolerance to be established upon this error will not 
be exceeded, then the buyer of the machine may make his deci- 
sions, drawing a proper balance between the speed of operation 
and the other at least equally important factors involved. 

In conclusion, with respect to the three types of error just dis- 
cussed, it will be seen that the wheel machines show a very definite 
dependence upon the outline or figure of the hide measured, or in 
other words, that two hides of identical area but differing outline 
would be differently measured by such a measuring machine, the 
greater reading being obtained in the case of the hide of the more 
irregular outline. The first two causes produce an error which is 
increased by increasing acuity of the angle which a part of the 
outline of hide makes with the plane of the corresponding measur- 
ing wheel, while the third cause is dependent upon the jaggedness 
of the outline in the sense that the error is increased by interrup- 
tion of the hide surface by a reentrant angle of such character that 
the contact of the hide with a given wheel ceases for a space and is 



28 Technologic Papers of the Bureau of Standards 

then resumed. If the hide has cut-in portions, the normals of 
which lie in a general direction perpendicular to the direction of 
the motion of the hide through the machine, the sort of action 
referred to will take place, in which one or more wheels are lowered 
out of engagement with the accumulating gears, and then later 
lifted so that the accumulating movement is reinitiated. 

(4) Effect of Thickness of Material. — On most of the wheel machines 
in use, an error exists due to the variation of the thickness of the 
material being measured, which arises in this way: Assume that 
the traversing wheels and the feed roll are running in contact and 
that the pinion of the traversing wheel just fails of engagement 
with the corresponding accumulating gear; now, if an extremely 
thin piece of material, such as tissue paper, be entered into the 
machine, the traversing gear will be lifted at the moment the 
advancing edge of the sheet reaches the line connecting the center 
of the feed roll and the center of the traversing gear. The accu- 
mulating gear will at once start to rotate (assuming that the 
fit and alignment of parts of the machine under consideration are 
ideal, so that its accumulating gears can be engaged by an 
extremely small rise of the corresponding pinions). When the 
piece of thin material has entirely traversed the traversing wheel, 
it will pass out of contact with that wheel and permit it to be 
lowered from engagement with the remaining gears just at the 
instant at which the retreating edge of the sheet leaves the lines 
of centers of the traversing wheel and the feed roll. 

Now, consider the case of a thick sheet of material, say a heavy 
hide of leather. The traversing wheel and the feed roll will begin 
to separate at the instant the sheet of material makes contact with 
both of them (see Fig. 12), which will occur before the advancing 
edge of the thick sheet reaches the line connecting the centers of 
the measuring wheel and the feed roll. The accumulating gear 
will therefore be engaged and begin to rotate as soon as the first 
contact and consequent lift of the traversing wheel by the sheet 
has occurred, and as the sheet emerges after having passed under 
the traversing wheel that wheel will continue to turn and the 
accumulating wheel will continue its engagement until the retreat- 
ing edge of the sheet has passed some distance beyond the line of 
centers and out of contact with the feed roll and the traversing 
wheel. The effect of this action is that the traversing wheel will 
have turned through an angle which is greater than the length of 
the middle line of the strip which it is the function of the traversing 
wheel to measure, and the readings of the machine will be in excess 



Area Measurement of Leather 



29 



by an amount equal to the sum of the excess rotations which have 
been contributed by each of the traversing wheels engaged in the 
measurement. It will be seen that the magnitude of this effect for 
each traversing wheel is a function of the diameters of the measur- 
ing wheel and the feed roll, of the engagement clearance between 
the traversing wheel pinion and the accumulating gear, and of the 
thickness of the hide, the error being greater for thicker hides. 




The only method known to the author which will accurately 
and satisfactorily compensate for this error is to provide a means 
of lowering the feed roll so that the clearance between the pinions 
of the traversing wheels and the accumulating gears is made equal 
to the average edge thickness of the hides being measured at any 
one period. A graduated lowering device, so arranged that it could 
be operated to set an indicator at a reading to correspond to the 
measured thickness of the hide as determined by a suitable thick- 
ness gage would seem to serve the purpose. It is believed that 
s ome such arrangement as this is to be found on one of the foreign- 
made types of leather-measuring machines, of which only a few 
examples are in this country. 



2,o Technologic Papers of ike Bureau of Standards 

It is of course to be understood that the compensation obtained 
in this way can not be a perfect one on account of variations in 
thickness from hide to hide, and in fact in different parts of the 
same hide. It does not seem, moreover, that any machine using 
wheel contacts as its operating principle can provide complete 
compensation. 

(5) Variance Due to Imperfections of the Linkwork. — The chains 
which operate to translate the motion of the measuring gears into 
rotation of the index hand at the dial are very important elements 
in the accuracy or rather consistency of the performance, in that if 
the distance between any two given links of any chain does not 
remain accurately constant during the operation of the machine, 
a variant error will be introduced, which will appear on the dial 
as an error in the measurement of the area. 

In order to arrive at an idea as to the nature of this effect, it 
should be recalled that the reading of the machine at any time 
depends upon the total length of the chains which have not been 
wound up on the drums of the accumulating gears. Any action 
which would have the effect of changing the effective length of 
chain remaining unwound would, of course, proportionately affect 
the reading. 

Consider a length of any ordinary chain suspended by one end 
from a rigid support, and let the exact vertical height of a point on 
the lowermost link, with respect to any convenient datum plane, 
be measured by a sensitive measuring device, as by sighting a 
micrometer microscope upon a fine horizontal mark or a dot or tip 
applied to that link. Let the height of this mark be observed 
and recorded. Now, it is obvious that if the chain be simply 
shaken, or bent or swung, and again allowed to come to rest in the 
vertical, the height of the reference mark will have changed, due 
to more or less irregular changes in the contact relationships of the 
several links as seen in the sketch (Fig. 1 3) . This change in the 
effective length of the chain is a secondary result of the friction 
between the links, and produces what is termed "variance" in 
the indications of any instrument of whose mechanism it forms a 
part. 3 All types of chains are subject to this error, although, of 
course, its amount will vary with the type and dimensions of the 
particular chain under consideration. Even cords, which were 
once used as connectors in leather-measuring machines, show a 
very similar effect, due to the internal friction or elastic hysteresis 

3 Sec p. 750 of B.S. Scientific Paper 3 28, "Variance of Measuring Instruments," by the present author. 



Area Measurement of Leather 



3i 



in the fibers and strands. Another source of variance due to 
chain action, having a similar effect, will originate at the points 
where the chain makes contact with the pulleys and drums around 
which it wraps, as the result of a certain latitude in the disposition 




Fig. 13 

of the chain laterally as it enters into contact with the pullev 
groove as shown in Fig. 14. This lateral variation in position 
has the effect of slightly altering the effective or net length of the 
chain with respect to its contribution to the indication at the dial. 




Fig. 14 

The most invariant type of flexible connector available is an 
easily flexed, slender, flat (metallic) tape or wire, the internal 
friction of which will be very low, and the length of which will be 
correspondingly invariable. This type of connector should serve 
excellently for the purpose. 



32 Technologic Papers of the Bureau of Standards 

If a chain is used, a type should be chosen which is as little as 
possible subject to variability in the distance from link to link. 
While the individual variations from link to link may be very 
small in amount, nevertheless in the total length of chain involved 
in the numerous separate elements of a leather-measuring machine, 
these variations may at times sum up to a large value when reduced 
at the dial to an equivalent of area, as every link of every chain is 
liable to suffer a change in its contact relationships and so occasion 
a change in the effective length of the connections throughout. 
One machine examined uses a rather favorable type of chain, 
in that it is almost perfectly circular in cross section, and has a 
smooth, regular surface, both of which properties assure, in so far 
as possible, the uniform engagement of the chain with the pulleys 
over which it passes. This is a factor which, as has been shown, 
is also important in obtaining constancy of reading. 

Another source of variability in the mechanism of the wheel 
types of leather-measuring machines is the complexity and 
multiplicity of connections and contacts in the linkwork generally. 
It is to be recalled that, in a 5-foot length machine of a common 
make (this being the usual working length), there are 11 pin or 
hinge joints in each of 5 lever systems, or a total of 55 operating 
joints in the averaging levers alone. In addition there are an enor- 
mous number of separate turning pairs consisting of link contacts 
comprised in the 40 chains involved, 40 separate bearing units sup- 
porting the accumulating gear journals, making 80 individual bear- 
ing elements, besides a small number of joints in the dial mechanism. 

The importance of this variance inherent in the operation of a 
complicated mechanism can be judged when it is considered that, 
in the case of a rectangular leather sheet of 9.86 square feet area, 
an extreme variation or "spread" amounting to 5.1 per cent was 
observed in a series of 20 consecutive readings. These readings 
ranged between the wide limits of 9.85 and 10.35 square feet and 
this large value was practically duplicated in 2 sets of readings 
in the 20 referred to. Probably most of this variance is charge- 
able to the unavoidable mechanical imperfections of the mechanism 
or link-work, since the rectangular sheet favors maximum con- 
stancy of overrun error and a minimum variance due to the width 
of wheel rims, although, to be sure, under exceptional conditions 
the rectangular sheet might favor a high value of that portion of 
the variability having its source in excessively wide spacing of 
traversing wheels. 



Area Measurement of Leather 33 

No instrument maker would expect such a mechanism to give 
satisfactorily reproducible results. In other mechanical measuring 
instruments, whenever high complexity of mechanism is unavoid- 
able in carrying out the function prescribed, the utmost refinement 
in bearing and connector elements is provided for, when accurate 
results are desired — as by the use of ball bearings or conical pivots, 
by extremely careful fitting of parts with respect to bearing clear- 
ances, by substitution of tapes and similar flexible connectors for 
chains and links, etc. The necessity for modification of existing 
designs in these essential respects can be judged by reference to 
a later section, Variance, under the general heading "Determina- 
tion of Machine Performance. " 

Another source of variance arising in the elements of the mech- 
anism is that due to the ratchet and pawl action used in prevent- 
ing reverse rotation of the accumulating gears until they are reset 
to the zero position. It is clear that, with teeth of finite spacing, 
some retrograde motion will take place before the locking position 
is attained. This motion is subject to the laws of chance, and 
the error produced is equally likely to be positive or negative so 
that no persistent error results, but only another manifestation 
of variance, that ever-present enemy of accuracy. 

On one of the common leather-measuring machines there are 
about 550 teeth on each of the accumulating gears which serve as 
ratchets. As only a partial rotation of each of these wheels occurs 
in the traverse of a skin, it is seen that the proportionate variance 
due to tooth spacing is by no means negligible. 

Possible expedients for reducing this error are to use (1) finer 
(more closely spaced) ratchet teeth, (2) "stepped" or offset 
multiple pawls with the existing tooth spacing, (3) the so-called 
toothless ratchet or clamping ratchet. 4 

The last expedient does not totally eliminate the retrograde 
rotation, as might be supposed, since a certain small reverse move- 
ment is required before the locking becomes operative. 

The variance due to ratchet-tooth spacing, like that due to 
spacing of traversing wheels and the width of wheel rim, can be 
definitely calculated, from a knowledge of the tooth spacing and 
the equivalent of rotation of each accumulating gear in terms of 
area at the registering dial. The range of variance due to this 
cause, like that due to the others discussed, should be determined 

4 References on damping ratchets: Mechanics of Engineering and Machinery, Weisbach (Klein's trans- 
lation, 1S90) 3, Pt. I, Sec. II, pp. S73-S78; The Constructor, Reuleaux (Supplee's translation, 1904) pp. 158- 
162; Principles of Mechanism, Robinson, 1896, p. 296. 



34 Technologic Papers of the Bureau of Standards 

in advance, and restricted within a predetermined partial tolerance 
of error established as the maximum permissible limit of the 
magnitude of this effect alone. 

Recapitulation: Persistent Positive Errors. — A significant fact in 
relation to three of the sources of error detailed above, namely, 
that of excessive width of traversing wheel rims ; that of overrun 
of the traversing wheels; and that of the thickness of the material 
being measured; is that each tends to increase the readings above 
the true area, while the other two major sources of error (excessive 
spacing of traversing wheels and imperfections of the linkwork) 
are probably as likely to result in deficient as in excess measure- 
ment. On the whole, then, it may be said that any machine 
having any or all of the three faults in the first group named will 
tend to measure in excess. Any characteristic tendency of a 
commercial measuring device to give readings regularly in error 
in the same direction is to be sedulously restrained, and it is 
impossible to overemphasize the need for especial attention and 
study in the design of this apparatus, in order to eliminate 
wherever possible (and it usually is possible, though radical 
redesign may be necessitated) all individual sources of error 
having a persistent and positive tendency to introduce errors of a 
particular sign. 

This whole question of increased precision in the measurement 
of leather, which seems imperative in the light of the data of 
this investigation (as well as of those of the British investigation 
reported by the National Physical Laboratory) seems to the 
author so important that he would again emphasize the disparity 
between the precision attained in the measurement of leather and 
that in the measurement of other commodities of similar or less 
value. The average price of copper per pound is about one-half 
that of leather per square foot, yet no smelter or dealer would 
consider using, for purposes of purchase or sale, a weighing scale 
having the enormous inaccuracy or variability which is charac- 
teristic of the usual leather-measuring machines. In weighing 
scales, instead of allowing a plus or minus variation of from i to 3 
per cent, as has been tolerated in the case of leather-measuring 
machines, the variation and error combined are restricted to 
±0.2 per cent or less, depending upon the type. For a weighing 
scale used indoors, ±0.1 per cent is the combined allowance 
for error and variation, after the scale has seen service. The 
tolerance on a new scale used indoors, is set at one-half of this 
value, under the assumption that a smaller tolerance should be 



Area Measurement of Leather 35 

established on new apparatus to permit of the service tolerance 
being maintained for a reasonable period after the apparatus has 
been put into use. 

(6) Secular Changes in Hides and Skins. — The question of accu- 
rate measurement of hides and skins is complicated by the fact that 
the dimensions of these materials are far from permanent, in that 
they suffer considerable change in each direction from variations 
in temperature and humidity. The time available did not suffice 
for an analytical study of this change, but on one set of six typical 
calfskins received from a Massachusetts tannery, the changes in 
area from the time of the receipt of the skins at the Bureau was 
considerable, ranging in amount for the several skins from 1 to 
2}4 per cent approximately, in a period of 37 days. 

It is by no means certain that these changes are reversible ones. 
It is quite probable, in fact, that a portion, at least, of the changes 
shown is due to a secular transformation which takes place in the 
material subsequent to the manufacturing process. The nature 
and character of this change will probably be more significant to 
leather technologists, and is here dismissed without further con- 
jecture as to its causes and the degree of its dependence upon the 
processes of manufacture. 

III. METHODS OF TESTING LEATHER-MEASURING 

MACHINES 

I. FORM AND MATERIAL OF THE AREA STANDARD 

Field calibration of leather-measuring machines requires the use 
of standards of area. The primary requisites for such standards 
are the following : (a) Thickness sufficient to raise into operation 
the traversing wheels of the usual types of leather-measuring 
machines; (6) A surface offering a reasonable tractive resistance, 
so as to drive the traversing wheels without appreciable slip; 
(c) An outline typical, in so far as may be, of the outline of the 
hides and skins usually measured ; (d) High permanence of dimen- 
sions under (1) changes in temperature; (2) changes in humidity; 
(3) the distortion due to the stresses incident to use; (e) Durabil- 
ity or resistance to mechanical wear. 

The first of these requires the use of a material comparable in 
thickness to ordinary upper leather, say 0.06 inch (1.5 mm) or 
more. The second requirement is fulfilled by any flexible material 
similar to leather or cloth having a surface giving a reasonable 
friction against the metals. This requirement eliminates mate- 
rials like the pyroxylin plastics, such as celluloid, and very thin 



36 Technologic Papers of the Bureau of Standards 

sheet metals, other properties of which might seem well suited 
to the work. 

Sheets of leather, as has been shown in the foregoing section, 
are far from permanent in their dimensions. Leather is decidedly 
affected by variations in humidity, and doubtless, also, to a large 
degree by variations in temperature. In addition it is to be 
expected that the deformations to which a sheet is subjected in 
the testing of leather-measuring machines would alter its dimen- 
sions gradually were it made of a material having the low elastic 
constants and relative "plasticity" of leather. 

In seeking for materials which should give promise of the best 
properties for this use, the following were suggested, but time 
has not been available to determine their physical constants in 
order to make certain their adaptability for this purpose. In 
order of their probable serviceability these two should be given 
consideration : 

1. A pyroxylin-coated textile material of the type now much 
used in the manufacture of artificial leather. Rough measure- 
ments made upon a small sample of this material indicated fair 
permanence under changes in humidity. It is to be expected that 
its thermal expansivity would be high, like that of many other 
organic substances. A question still to be investigated in mate- 
rials of this sort is the obtaining of the necessary thickness. 
This should offer no difficulty if the manufacturer of artificial 
leather does not object to coating a special, heavy fabric. 

2. Rubber or composition sheet packing containing an inserted 
wire fabric. Mateiial of this character, using a brass-wire fabric, 
is already on the market as a high-pressure steam packing. 

This material can be produced in almost any desired thickness, 
is reasonably flexible, and should be quite durable in use. 

The determination of the essential properties of either of the 
two materials suggested above will be a simple matter; the coeffi- 
cients of expansion under varying humidity and varying tempera- 
ture are easily and quickly measured. 

With regard to the form of the test sheet, careful experiments 
have shown that the outline of the area measured affects the read- 
ing of the machine, this arising, as has already been explained, 
from the effects of overrun in the mechanism, the width of travers- 
ing wheel rims, and the spacing of the wheels. On this account it 
will not be satisfactory to test leather-measuring machines with 
sheets of rectangular or circular outline as was customary up to 
the time of the Bureau's investigation. With areas of such outline 



Area Measurement of Leather 



37 



but a single engagement and a single disengagement of any given 
traversing wheel will take place, whereas with the ordinary skin 
twice as many engagements and disengagements of some wheels 
may occur. Moreover, a right-line perimeter does not develop 
the variance due to excessive width of wheel rim and to exces- 
sively large interval between wheels. That this is the case, will, 
of course, be quite clear from the paragraph above, concluding 
the discussion of the first three types of error of the wheel machines. 
The results of the analytical investigation of the performance of 
leather-measuring machines described in the first section of this 
paper showed clearly that the use of rectangular test sheets was 
resulting in the certification or acceptance by weights and measures 
authorities and by the manufacturers, of machines which were 
affording apparently satisfactory results when used with such 
standards of area, but which, as it developed, were subject to 
very large and intolerable errors when used on the irregularly 
outlined figures of the actual hides and skins. 




AREA=2a 2 



T 




Fig. 15. — Original form of area standard developed at Bureau of Standards , later replaced 
by the type shown in Fig. 16 

As a result of these deficiencies of the usual type of test sheets, 
an attempt was made to design an outline which would afford a 
rough approximation to the figure of a hide or skin, and which 
should, at the same time, be easy to prepare and to calibrate. 
With this in view, the outline denned in Fig. 15 was designed, 



38 



Technologic Papers of the Bureau of Standards 



but since that time Max Sasuly of the Bureau of Standards has sug- 
gested and laid out an outline of improved form. This, shown in 
Fig. 1 6, is equally easy to prepare, while on account of its more ob- 

















M 




4 


1 
) 




> 






—?/ t 








^^ 


< 








Z0J< 








> 






< ! 




- 1 **- 








l /\ 




f 

a 

\ 






— 
















GENERAL AREA 5TANOW0 




| 












B IO-49 

















N/1 










> 






< 








%». 


,-; 




j 




y 




-< 








k\ 










UtQE 


1 




s ^™, 




i 


i 










Bi052 




r AR£A STPJIOARD 

















M 








2 






< 








ORE 


zo-n 




i. 




i 






< 


t. 






PN 








1 U "h^ 














£OFT AREA STAMWRD 






, 










e io5o 



Fig. i6. — Latest type of area standard 

As compared with that shown in Fig. is. this has the advantages of greater durability, more effeetiye out- 
line characteristics, and greater ease of preparation. The first figure given is a general or type standard in 
which the dimensions are given algebraically; the other three are calculated for specific areas of 5, 10, and 
20 square feet, respectively. 



Area Measurement of Leather 39 

tuse angles and rectangular boundary, it is less likely to become 
frayed in service, and will be more readily guided through the meas- 
uring machine. It will be noted that while the outline affords the 
desired irregularity, the area is, nevertheless, a very simple function 
of its leading dimensions. The following is excerpted from the 
discussion which was sent out by the Bureau, accompanying blue 
prints defining these new standards of area, at the time the in- 
formation regarding thern was given to the leather trade (Decem- 
ber, 191 7) : 

With reference to the question of standard patterns for testing leather-measuring 
machines, we would say that since our previous correspondence with you, we have 
developed another style of pattern which has certain advantages over the star-shaped 
pattern originally recommended (our report to the Massachusetts Commissioner of 
Weights and Measures, under date of Feb. 5, 1017). Blue prints showing the relative 
dimensions of this new design, and showing the particular dimensions for suitable 5, 
10, and 20 square foot areas, are inclosed. One advantage of this style is that there 
are no projecting acute-angled corners that are liable to be bent in handling. Second, 
the patterns can be made from paper of common integral sizes, 2, 3, and 4 foot widths, 
which is more readily obtainable and has its edges cut parallel. Third, the dimensions 
are nearly all integral values, so that the laying off of the pattern involves no difficult 
measurements nor the use of special scales. 

You will note by the shape of the design that the pattern is most readily cut by laying 
off on the rectangular sheet of paper of the required size, parallel lines at distances a and 
2a from each end, where a is one-sixth of the total length or one-fourth of the 
width; also two lines parallel to the sides at a distance a from the sides. The inter- 
sections of these lines with the edges then serve as the points from which six triangles 
are cut out of the rectangular piece of paper, the apices of these triangles being at equal 
distances from the edge of the paper in each case. It is not necessary for correctness 
of area, though it is for the sake of uniformity of outline, that these triangles be isos- 
celes — (that is, that they have two sides and two angles equal) provided the sides meet 
in the lines at the distance a from the edge of the paper. The area of each triangle 
will be its base (either a or 2<z) times one-half the height (K a )- 

In the suggested form for a 10-square foot area inclosed, the general form is varied 
slightly in order to use integral foot dimensions for the rectangular sheet of paper, 
making use of a 3-foot width of paper, and to use integral lengths for the bases of the 
triangles (1 and 2 feet), while the heights of the triangles are in each case 6 inches. 
Another feature of this design is the drawing on the pattern of four lines which may 
be called normal or control lines, inasmuch as they are used as a means of checking or 
proving the area of the pattern. Two of these lines extend lengthwise of the pattern, 
parallel to each other, and should have a length of about five-sixths of the length of 
the pattern. The other two extend across the pattern and should have a length of 
about ten-thirds of n. The lengths for these lines are shown in the illustrations. 
They should be measured at the same time as the other dimensions of the pattern are 
measured, and after the pattern has been cut the measurements should be marked 
on the pattern in each case. The exact area of the pattern as computed from measure- 
ments made at the same time should also be marked plainly on the pattern. Then, 
occasionally, in future use of the pattern, the control lines should be measured, prefer- 
ably with a steel tape graduated to tenths of inches. The amounts by which these 
measured lengths differ from those shown on the pattern should be averaged for the 
longitudinal lines and for the transverse lines separately, and the percentage which 



40 Technologic Papers of the Bureau of Standards 

these amounts are of the total lengths of these two sets of lines respectively should be 
computed. These two percentages when added together algebraically will be the 
percentage by which the area of the pattern, under the conditions at that time, differs 
from the area marked on the pattern. 

For example, suppose in the case of the 20 square foot area, the lengths of the longi- 
tudinal lines drawn on the pattern were 60.02 and 60.05 inches, respectively, at the 
time the pattern was made, while those of the transverse lines were 40.01 inches and 
40.07 inches, respectively, and that the then calculated area of the pattern is 20. or 
square feet. If, at some later use of the pattern, the lengths of the first two lines are 
60.12 inches and 60.13 inches, the changes in these two lines will be 0.10 inches and 
0.08 inches, respectively; giving an average increase of 0.09 inches, or 0.15 per cent. 
Likewise, suppose that the measured lengths of the transverse lines at this time are 
40.16 inches and 40.24 inches. The changes in these lines will then be 0.15 inches 
and 0.17 inches, an increase of 0.16 inches or 0.4 per cent. All of these changes 
are increases; hence, adding together 0.15 per cent and 0.4 per cent, we have 0.55 
per cent as the change in area of the pattern. In other words, the pattern will be 
0.1 1 square feet larger under these conditions than when it was standardized; that is, 
its area when in use at the time of the later measurements above detailed will be 20.12 
square feet. 

It is desirable to have these pairs of base lines at right angles to each other as the 
expansion and contraction of paper with changes in humidity are different in the two 
directions of the sheet. Two lines in each direction are suggested, as an average of 
two will give more accurate results. It may be found, however, that the measure- 
ment of one line in each direction will be sufficient for most purposes. In such cases, 
however, the percentage change of each line should be computed in the same way 
and the results added together to give the percentage change in area. 

For the original measurement of the pattern, it is suggested either that the parallel 
lines at distances a and 2a from the ends and sides be drawn carefully, that is, as 
straight and as parallel to the edges as possible, and that the distance of these lines 
from the edge of the paper at each side of each triangle be measured with a steel rule 
or tape and the mean of each pair of such measurements be used as the height of the 
triangle in question, provided, of course, that the triangle has been so cut that the apex 
lies in the line at distance a from the edge of the paper; or a straightedge may be laid 
in coincidence with the edge of the paper on each side of the corners of the triangle 
and the height of the triangle measured by means of a steel square laid against this 
straightedge and passing through the apex. The length and width of the sheet should, 
of course, be measured at both ends and sides, and the average taken in each case, 
and the bases of the triangles should be measured along the edge of the paper. The 
total area can then be found by subtracting from the rectangle of the sheet the sum 
of the areas of the six triangles as obtained by multiplying their bases by one-half 
their heights. A suggested form of computation is appended, with sample dimensions 
inserted to show the method of calculation used. 



Area Measurement of Leather 



4i 



TABLE 3. — Sample Form of Computation of Areas of Patterns for Testing Leather- 
Measuring Machines 



First 

measure 

ment: 



Second 

measure' 

ment: 

right 

side, 
inches 



Length of rectangle 

Width of rectangle 

Area of rectangle 

Base triangle A 

One-halt base triangle A . . . 

Height triangle A 

Base, triangle B 

One-half base, triangle B. . 

Height, triangle B 

Base, triangle C 

One-half base, triangle C. - 

Height, triangle C 

Base, triangle D 

One-half base, triangle D.v 

Height, triangle D 

Base, triangle E 

One-half base, triangle E- . 

Height, triangle E 

Base, triangleF 

One-half base, triangle F. . . 

Height, triangle F 



72.06 
47.98 



72. 02. 
48.02 



72.04 
48.00 



24.01 
12.005 
11.99 
12.00 

6.00 
11.98 
11.98 

5.99 
12.00 
24.00 
12.00 
12.00 
12.04 

6.02 
11.98 
12.00.. 

6.00 
12.00 



Total area of six triangles - 



Area of pattern=3467.92— 576.42=2881.50 square inches=20.01 square feet. 

A set of three test sheets of 5, 10, and 20 square feet area, re- 
spectively, and possibly one of 30 square feet, should be provided 
for the regular use of the inspector of leather-measuring machines. 
For the larger machines occasionally found, suitable sheets up to 
the 60 square feet capacity will have to be provided. It does not 
appear that the use of several sheets in succession, in order to 
obtain a calibration of the upper range of capacity, can at present 
be considered satisfactory, as the effect on certain of the machine 
errors, as involved in the traverse of a succession of separate 
sheets, has not been investigated. It might be suggested that a 
standard of area should be designed such that its perimeter would 
fit into that of another standard, so that two or more such 
standards could be passed through the measuring machine in such 
a way as to form a practically continuous sheet. It does not 
appear, however, that this is a practicable solution at the present 
time, and the best expedient seems to be the use of an adequate 
number of standards to obtain by their use singly, a calibration 
of the machine over its full range of graduation. 



42 Technologic Papers of the Bureau of Standards 

The sheets, when rolled up, may be carried in cylindrical fiber- 
board or metal tubes, which will serve to protect them from the 
weather and the rough handling incident to transportation. 

2. DETERMINATION OF MACHINE PERFORMANCE 

In any measuring instrument, accuracy, or accordance of the 
indication with the true value of the quantity measured, can be 
manifested in either one of two ways. (True or perfect accuracy in 
any measurement does not, of course, exist, and only a relatively 
high, or substantial exactness is implied in the present use of the 
term.) 

i. An invariable and consistently reproducible correctness of 
indication on all successive determinations made at every value 
of the quantity being measured. This may be termed " invariant 
accuracy." 

(2) Errors of varying magnitude and sign, which appear as devi- 
ations about the true value of the quantity being measured, such 
errors having, however, a mean value which, when a large num- 
ber of observations are taken, becomes equal to zero. Performance 
of this sort may be termed "group" or "statistical" accuracy. 

Unfortunately, the above distinctions have not in the past been 
used as the basis of discussions of measuring instrument per- 
formance, and much confusion has resulted. Instruments have 
been treated as simply inaccurate when in point of fact they were 
highly variant. The high variance may easily be of far greater 
importance than a high invariant inaccuracy, as it is clear that 
almost any instrument can be corrected, either by adjustment of 
its mechanism, or by suitable regraduation of its dial, to give pre- 
cisely accurate readings, if only its reading at any given value of 
the quantity measured, is consistently reproduced in subsequent 
determinations. The latter condition can never, of course, be 
fulfilled in practice, as all instruments are subject to more or less 
unaccountable and unsystematic variations under the conditions 
of ordinary use. Thus a weighing scale used to weigh the same 
load repeatedly, will never give identical successive readings of 
the weight, but will show more or less variation about a mean 
reading, which latter, however, is likely to be quite a definite and 
stable value, becoming more definite as the number of observa- 
tions entering into the average is increased. 

With these considerations in mind, it is seen that in the con- 
struction of a leather-measuring machine very precise results 
would be assured if it were possible to eliminate practically all the 



Area Measurement of Leather 43 

variance, as the correction of the remaining inaccuracy would in- 
volve only the simple matter of regraduating the dial or changing 
the length of an adjustable lever or cam or similar element. The 
problem, then, is reduced to one of diminishing the variance to 
such an extent that the errors of all readings of the machine will 
he within the established tolerance, or, as might perhaps be a more 
rational though less simple mode of specification, that the average 
deviation from exact reading shall not exceed a certain other, and, 
of course, smaller tolerance. 

In order to select, then, from a group of several measuring ma- 
chines, that type which can be expected to afford the most reliable 
results, the criterion should be reproducibility or invariance of 
reading rather than accuracy of reading in the ordinary sense of 
the term. As has been stated, all commercial measuring instru- 
ments are subject to sensible variation in reading, and while it is 
conceivably possible to adjust the average performance of the 
instrument over any considerable period of operation to such ac- 
curacy that no general or extensive aggregate error or economic 
loss would be engendered, nevertheless, to provide against large 
individual errors, and to prevent serious injustice in occasional, 
accidental cases, the basis of selection of the instrument should be 
the range of variation of reading at particular values of the quan- 
tity being measured, or the average deviation from the mean read- 
ing corresponding to particular values of the quantity being 
measured. 

By way of example, it may be stated that differences as high as 
4.3 per cent have been noted in the case of readings in the same 
series on the same area on one common type of leather-measuring 
machine. Two other machines gave extreme variations of 2.3 
per cent and 1.3 per cent, respectively. 

The accuracy of a measuring device depends upon the adjust- 
ment to which it was subjected by the maker and, within reason- 
able limits, the mean of its readings can by proper care at the time 
of test, be adjusted to be, at that time, practically coincident with 
the true value of the quantity measured. The deviation of suc- 
cessive observations from these mean readings, however, is not 
subject to improvement by adjustment, and in that sense is not 
the result of mere casual circumstances or accidents in the adjust- 
ment of the instrument. 5 It represents rather the effect of de- 
sign and workmanship upon the readings, and forms, therefore, a 

6 See ' 'TheConcept of Resilience with Respect to Indicating Instruments." by the present author; Jour- 
nal of the Franklin Institute, February. I9r9; pp. 166-167. 



44 Technologic Papers of the Bureau of Standards 

criterion by which machines of diverse types can be differentiated, 
as compared with the accuracy of individual readings, which is 
best employed to differentiate between several machines of the 
same type and quality. 

The problem in hand, then, in the case of leather-measuring 
machines is to select that type which is capable of most accurately 
reproducing its readings in successive measurements of the same 
area, and such selection can be made on the basis of a group of 
readings given by the instrument when it is operated repeatedly, 
using the same area standard. 

This criterion may be expressed numerically by the use of the 
" average deviation of the readings from the mean " which, assum- 
ing a group of readings taken by successive operations of the ma- 
chine on the same area, is obtained as follows: (i) Compute the 
average of the observations obtained by successive measurements 
of the same area made under the same conditions; (2) Compute 
the difference between each of the several observations and the 
average of the group. These differences are the deviations or de- 
partures of the several observations from the mean. The sum of 
all the deviations divided by the number of observations is the 
"average deviation from the mean." 

This method of analysis permits the determination also of the 
probability or chance that any machine will give a preassigned 
deviation from the mean or average value of its successive read- 
ings, and also the probability that any deviation from the mean 
shall be greater or less than any given amount. For example, it 
has been deduced that one make of machine will commit a devia- 
tion or error of 1 per cent or more, about 60 times in 1000 opera- 
tions, while a certain other make will commit an error of that 
magnitude about 360 times in 1000 operations, these conclusions 
applying to determinations made with a 10-square-foot test 
sheet of the later Bureau of Standards' design applied with its 
long axis moving perpendicularly to the common axis of the travers- 
ing wheels. By this method of calculation, very definite differ- 
ences in performance were developed between three makes of 
machines investigated, their ratings on a scale of average devia- 
tion from mean reading being represented by the series 0.34, 
0.42, 1.07; the smallest number, of course, which represents the 
smallest average deviation from the mean, corresponding to the 
highest rating as to repeating accuracy. The mean errors of the 
same three machines were, taken in the same order as the fore- 
going, 0.7 per cent, 0.6 per cent, 1.5 per cent. 



Area Measurement, of Leather 



45 



To repeat, it may be said that the mean error could be diminished 
practically to zero by a suitable change in the adjustable parts of 
the machines, or, more generally, by recalibration of the dial. 
This would leave the machines comparable strictly upon the basis 
of the average deviation from the mean reading, which would 
necessarily, of course, be combined in the final decision, with num- 
bers expressing excellence in respect to other qualities, such 
as smallness of errors due to overrun, width of tires, spacing of 
wheels, thickness of sheet, etc. Numerical expressions for all 
these effects can be obtained and a combination of these num- 
bers into one number, the several components being suitably 
weighted according to the importance which each is considered 
to possess, will then be made, affording a single significant number, 
which may be called the figure of merit of the machine. 

The following table gives the results of a series of variance 
determinations made on three leather-measuring machines, show- 
ing the steps in the calculation and the nature of the numerical 
results arrived at: 

TABLE 4. — Bureau of Standards Test of Three Leather-Measuring Machines at 
Danversport, Mass., Aug. 22, 1918 

[All determinations made with long ails ol test area moving perpendicularly to common axis ot traversing 
wheels. Test sheet used: Bureau of Standards type (Fig. 16)] 





Machine I 


Ma- 
chine 11 


Machine m« 




c*) 


(<0 


m 


1 


2 


3 


4 












10.01 
10.02 

9.97 
10.04 
10.03 
10.00 
10.00 

9.96 
10.07 
10.05 
10.12 

9.97 






Successive readings of the several machines 


10.00 
10.02 
10.13 
10.07 
10.13 
10.13 
10.18 
10.02 
10.17 
9.93 


10.10 
10.24 
10.25 
9.87 
10.25 
10.05 
10.30 
10.06 
10.05 
10.10 


10.12 
10.05 
10.00 
10.06 
10.04 
10.07 
10.09 
10.10 
10.02 
10.13 


9.95 
10.08 
10.18 
10.07 
10.01 

9.97 
10.06 
10.13 
10.15 


10.08 

10.20 
10.07 
10.09 
10.04 
10.09 
10.02 
10.07 
10.07 


10.02 
10.02 
10.10 
10.06 
10.03 
9.93 




10.11 
10.02 
10.11 
10.03 
















Mean 


10.08 
.92 
.70 


10.13 
1.53 
1.07 


10.07 
.68 
.34 


10.07 
.84 
.61 


10.02 
.37 
.35 


10.08 
.78 
.31 


10.04 




.57 




.43 








2.5 


4.3 


1.3 


2.3 


1.6 


1.8 


1.9 







»i, 2, 3, 4=Forty observations taken by the author. August, 1918. 

6 Ten observations taken by J. J. Cummings, March. 191S. 

' Ten observations taken by the author on same machine in August. 1918. 

Mean of 40 observations 10. 05 

Average deviation, 40 observations P er cent . . .42 

Extreme variation , 40 observations do ... . 2 . 70 

Check measurements on the test sheet show that its actual area was. sq. feet. . 10.04 



46 Technologic Papers of the Bureau of Standards 

3. ACKNOWLEDGMENTS 

In connection with this investigation it is a pleasure to acknowl- 
edge the hearty and effective cooperation which the author has 
received from a number of sources. H. M. Roeser, Assistant 
Physicist of the Bureau of Standards, who is a specialist in the 
theory of errors, has afforded most valuable cooperation in draft- 
ing and carrying out the methods for the calculation and numerical 
expression of the variability of leather-measuring machines. E. 
C. Laughlin, assisted by E. W. Shippee, V. A. De Castro, and 
T. M. Cockrill, all of the staff of the Bureau of Standards, carried 
out with painstaking care and accuracy, the very extensive series of 
measurements and calculations required to establish the areas of the 
six hides used as tentative reference standards in the early part of 
the investigation, as well as much of the computation involved in 
some of the later work regarding the errors due to overrun, etc. 
Both the National Boot & Shoe Manufacturers' Association and the 
National Tanners' Association have furthered the work in a most 
enthusiastic way, and especial mention is due, respecting the 
courtesies extended by W. H. Denham of the former and Walter 
Creese of the latter organization. J. J. Cummings, of the staff of 
the commissioner of weights and measures of the State of Massa- 
chusetts, lent continual assistance during the field work in Massa- 
chusetts, and took a number of observations which were needed in 
connection with the studies being made of the amount of the 
inherent variability of leather-measuring machines. Mr. Day, 
of the same office, also aided in the field work. To these and to 
the tanners, leather dealers, and shoe manufacturers who made 
possible the inspection of their measuring equipment and methods, 
and all others who have furthered the investigation, the author 
is happy to express appreciation on behalf of himself and the 
Bureau of Standards. 

IV. SUMMARY 

The scant literature on the subject of leather-measuring 
machines is reviewed, and the facts which called for the carrying 
on of the present investigation are reported. The importance of 
the problem of leather measurement from the commercial point 
of view is indicated, as it underlies the sale of 900, 000, 000 square 
feet, or more than $400 000 000 worth of hides and skins annually 
in the United States. The principles of design involved in leather- 
measuring machines are set forth in detail with respect to the 



Area Measurement oi Leather 47 

kinds in common use. An analysis is made of the sources of the 
serious errors which commonly exist in commercial leather- 
measuring machines of the wheel type, including the effect of 
width of traversing wheel rim, of overrun of the wheelwork, of 
varying thickness of the material measured, of imperfections and 
mechanical complexity in the linkwork, etc. Attention is called 
to the fact that a number of the sources of error definitely favor 
overmeasurement, so that, on the whole, the common leather- 
measuring machines will tend to measure constantly in excess. 

A design for standards of area, which eliminates the disadvan- 
tages of the simple rectangular and circular outlines hitherto 
employed in the testing of leather-measuring machines, is pre- 
sented, and a complete outline of procedure for the conduct of 
performance tests on these machines is laid down. Distinction is 
drawn between accuracy which is evidenced as an invariable cor- 
rectness of indication, and accuracy which appears as correctness 
in the mean value of variant indications, and it is shown that 
variancy of indication may be a far more serious fault than simple 
inaccuracy, since the latter can be corrected for by adjustment 
of the machine, while the former, generally speaking, can not. The 
paper indicates a means of obtaining a numerical comparison of 
measuring machines with respect to the variancy or lack of con- 
sistency in their readings, and gives in tabular form the results of 
variance tests on three wheel machines, showing typical calcula- 
tions of the essential factors. 

Washington, August 19, 1919. 



